During the early design process, simulations allow numeric assessment and 3D models allow visual inspection for qualitative criteria. However, exploring different design alternatives based on both is challenging. To support the design exploration of quantitative performance and geometry typology of various design alternatives during the early design stages of indoor arenas, this paper proposed a novel design method of SOM-MLPNN by combing self-organizing map (SOM) and multi-layer perceptron neural network (MLPNN), based on the inspiration of local linear mapping based on self-organizing map (SOM-LLM). In SOM-LLM or SOM-MLPNN, the SOM can support designers to explore the whole design space according to geometry typologies and provides reference/labelled inputs for LLM/MLPNN to approximate multiple quantitative performance data for various design alternatives. Both SOM-LLM and SOM-MLPNN are applied and compared in a design of indoor arena. Besides the development of the method, original contributions include 1) proposing two operations (using a large size of SOM network and using a small amount of input data to train the SOM network) to save the computational time and increase the accuracy in data approximation and 2) proposing a series of data visualizations to interpret the results and support design explorations in different ways.

Indoor multi-functional sports arenas are a complex building type. Integration of the (multi-) functional space and of the large-span structure of the roof mainly determines the overall geometry of the building, and is one of the most challenging phases of the design. Several interdisciplinary numeric assessments and numerous solutions with diverse geometries (rather than just several specific types) should be considered to make informed design decisions. To support the design exploration in the early design stage for multi-functional arenas, this paper proposes a design process that is composed of a flexible parametric model, a framework of interdisciplinary assessment criteria, and multi-objective optimization (MOO) with post-process tools. The parametric model is defined based on the basic spatial composition of arenas and is flexible to provide a broader design space, including diverse solutions with three frequently-used structural types. The framework of assessment criteria includes indicators of viewing quality for spectators, acoustics, and structures, which can evaluate the design in different aspects. Based on certain assessment criteria, the MOO can be used to search for good designs in the broader space, and the post-process tools facilitate the designer to analyse the results. Two typical arenas (the Barclay Centre and the O2 Arena) are selected as real case studies to demonstrate the proposed process and assess the capacity. Results of the case studies validate the efficacy of the process and the necessity of the broader design space to include diverse solutions with multiple structural types.